7/29/07

i suggested in a previous blog post that my earlier view that only universals license exceptives may be wrong, because a range of determiners and combinations of determiners and either cardinals or certain adjectives appear to license exceptives as well. now i'm going to suggest once again that it may just be universals. i will suggest that every construction that licenses exceptives falls into one of the following categories:

1. a quantifier that is a universal on its face (ex. every)2. a quantifier that is not universal on its face, but is logically equivalent to a universal quantifier (ex. no)3. a non-quantificational construction that can nonetheless assert a universal (ex. thetallest)4. a construction that admits of a presupposed partition, with (implied) universal quantification over the partition's elements.

the first category is mostly obvious. what i take it to include which may be not obvious is generics, which are arguably not universal on their face because they have no face - i.e. they are invisible. i am talking about sentences like the following:

bears are godless killing machinesmary takes aspirin in the morning

i take these to be universal statements over typical instances of bears, in the first example, and mary's mornings, in the second. i won't defend this view here; i may defend it elsewhere.

the second category - of quantifiers logically equivalent to universals - is mostly there to capture negation. negative quantifiers are usually translated as negated existential quantifiers, but they are logically equivalent to universally negated sentences. for example, nobody loves you is typically translated as it is not the case that for some x, x loves you. but it can also be translated as for every x, it is not the case that x loves you. given this translation, we have a universal for the exceptive to leech off of.

sentential negation also admits exceptives, as in mary hasn't kissed john, except last new year's. in davidsonian semantics and its neo- and semi- varieties, sentential negation can be seen as negative quantification over the sentence's event argument. so the last sentence can be translated for every past event e, e is not an event of mary kissing john, except event e' last new year's. so sentential negation falls in this category too. negative polarity any falls in this category as well. free choice any can fall in this category or the last one, depending on how you look at it - you can consider it facially a universal or just translatable as one, as you fancy.

the third category consists of non-quantificational structures that can carry quantificational meanings, like the five, the tallest, and the only. i will suggest that this is where zamparelli's analysis starts to become relevant. it's also where i start to go out on a limb. what i'm going to claim here is that unlike ordinary the, the in these cases includes a universal component. zamparelli's analysis makes this somewhat plausible, because it allows us to associate universal quantification with the strong DP syntax rather than making it a purely lexical phenomenon. what i'll suppose is that inherently quantificational determiners like every are necessarily found in SDP, the strong determiner phrase; some determiners, like some, can never be universal for semantic reasons, and they must appear in the predicative determiner phrase, PDP; and others, like the and perhaps few and many, can appear either in SDP or PDP, and receive an interpretation accordingly.

zamparelli noted that the possessive can be predicative or non-predicative, depending on whether it is followed by a cardinal or not:

these are my toys. those are my toys too.*these are my three toys. those are my three toys too.

in the first sentence, the possessor my is in PDP, which allows an empty SDP (or allows SDP not to project), so there is no uniqueness requirement on the possessive. in the second sentence, the possessor is forced to SDP by the presence of the cardinal, which imposes the uniqueness requirement, shown by the unacceptability of adding the second sentence. the same would be true if "three" was replaced by "only" or any superlative.

i'm suggesting that the same happens with the. it is located in PDP unless there is something like a cardinal, a superlative or only to force it into SDP. as a consequence, the is not universal in the boys, but is universal in the three boys or the tallest boys, allowing these phrases to license exceptives.

two problems arise: first, what is the if not universal? presumably it is a group. the collective/distributive analysis of definites is well known. i suggest that when the is in PDP, it has a collective, group, interpretation, which does not require asserting something of all the members of the group. in PDP, the has a distributive, universal, interpretation. i wish i could say i have independent evidence for this analysis. maybe i'll get some for christmas.

second, there's the fact that the in SDP is not downward entailing in its first argument, casting doubt on the analysis that it is universal.

the five high schoolers helped out--/-->the five tenth graders helped out

this might be rescued by a von fintel-style strawsonian condition on entailment; or maybe we'll have to refine how we talk about universals and entailment in order to make this work.

what about few and many? if we follow partee's 1986 paper many quantifiers, these are ambiguous between a cardinal interpretation and a quantificational one. maybe the cardinals are in PDP and the quantifiers in SDP; or maybe paolo acquaviva's breakdown of quantifiers like few into negation + many engages the SDP layer through negation. it seems like i'm grasping at straws here, but ultimately i don't think these analyses are as implausible as they seem from my presentation. i'm a little ill and i've been writing all day, so give me a break.

the last category is of quantifiers that admit of presupposed partitions with implied universal quantification over the partition's elements. if you don't know what i'm talking about, refer to my previous posts here and here. what i suggest is that SDP licenses such presuppositions, so that quantifiers that appear in SDP can admit of these interpretations, and license exceptives, even though their semantics are not universal. this applies to most, as well as many and few when these are interpreted with non-cardinal meaning. cardinals, some, and a(n) can't appear in SDP so they never admit the presupposition interpretation.

this approach predicts that many and few can only allow the presupposed meaning on their proportional interpretations and not the cardinal ones. i contend this is true. care to contradict me?

many scandinavians have won the nobel prize, except finns

this should mean that for every scandinavian country, relatively many, but not necessarily absolutely many, nationals of that country won the nobel prize.

this approach raises the question of why the presupposition interpretation is not available with universals. i claim that it is, but you'd never notice it because it's logically entailed by the universal interpretation. for example, every high schooler helped out logically entails [presupposing a partition P of the set of high schoolers, for every element Q of P,] every x, x an element of Q, helped out. this is true for every partition P, so the presupposition is always utterly redundant, hence undetectable.

actually, i wonder if the universal interpretation of the can be brought in under this category, thereby eliminating the problems mentioned above. maybe the best interpretation of the tallest boys helped out is [given a partition P on the tallest boys, for every element Q of P] the boys x, x an element of Q, helped out. this seems to get the semantics right.

also, now that i think of it, aren't exceptives pretty okay with the when the sentence's predicate is highly distributive, but not when when it tends to admit of a collective reading?

having blue eyes is very individual, which highly favors the distributive reading which i'm arguing is associated with the universal interpretation and SDP, while lifting the table strongly suggests a collective reading, which is associated with a non-universal interpretation and PDP. maybe this whole analysis can be made plausible yet.

now what accounts for the Det friend that i have pattern? i hope it's not restrictions on movement, cause goddamn, i don't understand that stuff.

i'm trying to think through some issues raised by wilson v. monarch paper co., 939 f.2d 1138 (5th cir. 1991) and similar cases. in this case, a jury found, and the court system upheld, that a vice president of a company was entitled to millions of dollars in compensation for intentional infliction of emotional distress after being demoted to warehouse janitor. this raises many questions and thoughts that i'd like to explore in this post, and presumably return to as i think about it more. i guess for now i'll put things in point form, since my thoughts are scattered.

- intentional infliction of emotional distress is not an easy kind of case to win, because the standards for abuse are pretty high. in wilson, the required standard was that the offending conduct be so outrageous that civilized society should not tolerate it.

- how widespread is the attitude that it is humiliating to be a janitor? do janitors think so? if not, are they simply in denial, or was the jury wrong?

- or is it a situation where the jury believed that the former vice president would have mistakenly believed that it is humiliating to be a janitor, either because of his idiosyncratic personal beliefs or because of the beliefs prevalent in his social class? it seems unlikely that a jury would find IIED and a judge would uphold it based on beliefs particular to an individual or class, unless it is a class belief shared by the judge and the majority of the jury.

- just what is it, anyway, that makes it humiliating for someone to be a janitor? are the factors purely social or is there something innate to humans that makes such work inherently humiliating?

- if, as i assume, the humiliation of being a janitor is entirely or primarily a social fact, why is such a social fact constructed? and why is a remedy for this humiliation offered in the narrow circumstances of executive demotion, but not in the broader setting of a society that assigns some people humiliating jobs on a career basis? in other words, how does the view that civilized society cannot tolerate the demotion of an executive to janitor reconcile with the fact that the same (presumably) civilized society assigns many people to be career janitors? what does this tell us about the relationship between law and society?

- all this assumes that what the jury found to be humiliating was the job itself, not, say, the fact that the person was forcibly transferred from one job to another, or the fact that someone was removed from a lucrative job. this seems to be borne out: we can safely assume that no jury would find emotional distress for someone who was transferred from janitor to VP, if the judge even allowed the case to proceed to a jury; and the law makes it perfectly permissible to fire a high-level employee for no good reason - certainly it's not considered outrageous conduct.

- one conclusion that can be drawn is that in the eyes of the law, it is much better for a vice president to be fired than to be forced to choose between working as a janitor and quitting, which is always an option. can the conclusion also be drawn that it is better for people in general to not work at all than to work as a janitor? advocates of "welfare reform" suggest that it is more dignified to do any work than to do no work at all. but if this is true, why is it abusive to make a vice president choose between working as a janitor or quitting, but not abusive to simply fire him?

- one possible answer is that we believe in meritocracy: it is not unconscionable to have a society in which some people are forced to have humiliating jobs, because our society allows the individual some agency in determining his or her ultimate circumstances: people who are meritorious (by some definition that we need not look into right now) are rewarded with non-humiliating jobs, while those who are not meritorious must accept humiliating jobs. what is abusive is to improperly assign a meritorious person like wilson to a humiliating job.

- the problem with this is that it is very widely recognized that whatever role merit plays in determining one's job prospects, it is far from the only factor, and circumstances of birth are a major determinant of whether or not one will end up in a humiliating job. and while this fact is lamented among liberals, it is tolerated by them, while illiberals seem to have no problem with it. would such illiberals on a jury not have found for wilson? or is this further confirmation that reactionaries lack analytical and/or moral intelligence?

i encourage law-students-to-be to give cleveland, and particularly case western, a good look, on grounds such as the following:

- cleveland is a large legal market that is comparatively underserved by regional law schools; it's also not considered a choice destination by graduates of the national schools. in other words, graduates of cleveland-area law schools face less competition for local jobs than do graduates of comparable schools in comparable legal markets.

- salaries for legal jobs in cleveland are not much lower than in large markets like new york, washington or LA, but the cost of living is much lower.

- scholarships at case western have some of the most generous conditions on renewability that i've encountered. they are typically renewable if your grades are over 2.33 - in other words, if you're not at the very bottom of the class. this is on a curve with a roughly 3.10 median and 2.70 75% percentile in 1st year (and presumably somewhat higher in upper years).

this article talks about how cleveland is an awesome city to live in. the basic arguments are valid, but it overstates the case by not including some of cleveland's drawbacks, such as: it's the poorest big city in the U.S. by one popular measure.

7/27/07

a recent story in the forward reports that leaders of american labor unions are stepping up to support israeli apartheid by undermining opposition to it by british unions.

many union leaders have signed on to a letter by the jewish labor committee bashing* the growing movement for anti-apartheid divestment, boycotts and sanctions by british labor unions. these signatories unfortunately include ron gettelfinger, the head of my old union, the UAW. it also includes major unions like the AFL-CIO, right-wing unions like the IBEW and the teamsters, and some allegedly progressive unions like UNITE-HERE. notably absent are the SEIU and the left-wing unions such as UE, who tend not to join the frenzied mob when israel gets challenged.my old local, by the way, UAW local 2322 in western mass, overwhelmingly - in fact, unanimously, if i recall correctly - approved a resolution to support divestment back in 2003. unfortunately, in the UAW the wishes of the rank-and-file bear little resemblance to what's expressed by the leadership.

in britain, the attitude of unions is quite different. a number of them have passed resolutions calling for private sanctions against israel or for encouraging their branches to consider sanctions. in canada, a major public-sector union in ontario, CUPE, voted unanimously for sanctions. and of course, south african trade unions, whose membership has directly experienced apartheid and remembers the solidarity of international unions, is far in the lead in opposing israeli apartheid. as willie madisha, president of COSATU, south africa's congress of trade unions, says:

As someone who lived in apartheid South Africa and who has visited Palestine I say with confidence that Israel is an apartheid state. ... workers and democrats of the world ... heeded our call when we struggled against apartheid. Boycotts, disinvestments, and sanctions against the apartheid regime in South Africa hastened our march to democracy. Why should it be different for Palestinians?

--------* otherwise normal people often go crazy when israeli racism is challenged. at some point i may tell the instructive story of the hysterical reaction to the umass divestment campaign, including by many people who are considered respectable and who consider themselves progressive.

7/26/07

i've noticed a pattern among degree relations that calls for explanation. when i originally wrote this up for a term paper some five years ago, i came up with an unsatisfactory solution that was of little explanatory value. now, in the spirit of bertrand russell's words about it being a wholesome plan to stock one's mind with puzzles, i hereby record and publicly stock my puzzle. actually, there appears to be a theory of vector space semantics, applied to prepositions (of all things) that might present a solution to the puzzle. but i don't understand the formalism, so i'll leave it as a puzzle.

first question: what is a degree relation? well, it's the semantics corresponding to things like comparatives, which take two degrees and compare them. in english, these include the comparatives -er, more and less, as well as function words like so, such, too, and enough, as in john is too tall to operate an airplane, or mary is so tall that she bumps her head on lampposts. what degree relations do semantically is compare two degrees. for example, in the sentence above too compares the degree of john's height with the degree of height appropriate or permissible for operating airplanes, finding that the former exceeds the latter, or, more appropriate to the common view that degrees are extents on a scale and not merely points, that the maximum of john's height is greater than the maximum appropriate or permissible for operating airplanes. mathematically, degree relations can be characterized as functions from pairs of degrees to a truth value.

naturally, to be compared the degrees must be along the same scale. however, since chris kennedy's santa cruz dissertation, we speak of positive and negative degrees. john's height can be equivalently expressed with the adjectives short or tall.

john is taller than marymary is shorter than john

these sentences are logically equivalent, and both do the same thing: compare the degree of john's height with the degree of mary's height. they just do it from the perspectives of different sides of the height scale. tall starts from the low end of the scale and extends upward, making it a positive degree. short starts from the high end and extends downward, making it a negative degree.

with this distinction in mind, we can characterize the degree relations in terms of whether the two degrees they compare are of the same polarity or not.

consider the comparative:

john is taller than maryjohn is shorter than mary

here two degrees of the same polarity are being compared. they can both be positive or both be negative. it doesn't matter, as long as they're the same. we can see this by the fact that we are either comparing the maximum degree, in the case of tall, or the minimum degree, in the case of short.

the same is true of comparatives more and less. and it's true of too. consider:

mary is too tall to play basketball

this compares two positive degrees. it says the maximum of mary's height exceeds the maximum of the height appropriate to basketball-playing. if we substituted short, then we would compare the minimums.

other degree relations require opposite polarities.

john is tall enough to play basketballjohn is so tall that he can play basketball

both of these sentences compare the maximum of john's height with the minimum height appropriate for basketball. if we used short instead, both polarities would reverse and we would compare the minimum of john's height and the maximum height appropriate to basketball.

now that we have defined degree relations and classified them by whether they compare degrees of identical or opposite polarity, we arrive at the observation that forms the puzzle: same-polarity degree relations can be specified by an extent phrase consisting of a number and a measure, like three feet. opposite-polarity degree relations cannot.

john is three feet taller/less tall than maryjohn is three feet too tall to play basketball*john is three feet tall enough to play basketball*john is three feet so tall that he can play basketball

these facts appear intuitively to be nonaccidentally related. there is no obvious semantic problem: if a minimum and a maximum can be determined on the same scale, we are able to find the difference between them. in fact, we can syntactically circumlocute, thus:

john is tall enough by three feet to play basketball?john is so tall that he can play basketball, by three feet

okay, the latter is kind of awkward, but the point seems valid. what appears to be the problem is placing the measure phrase in the syntactically privileged specifier position in front of the degree phrase. and yet our intuition is that it is the semantics of degree relations that allows or disallows the measure phrase specifier.

good puzzle, no? chris kennedy liked it. i may one day read zwarts and winter's vector space semantics well enough to check for its applicability to the present puzzle. or perhaps someone else will come up with a solution.

7/25/07

tom mayer, a sociologist at the university of colorado boulder, has investigated the plagiarism allegations against ward churchill and found them to be "superannuated, unproven, substantively inconsequential, and either wrongheaded or misdirected."

the conclusion to his report is worth reading for its exposition of the moral cowardice of liberals - at least most of the liberals who prof. mayer has discussed the churchill affair with. those who observe the political scene will not be surprised. nor will they be surprised that the fascists who support the witch hunt deluged mayer with vulgar and inarticulate hate mail. as liberals are cowards, so are fascists idiots. the full text of the conclusion is below.

Procedural fairness in modern jurisprudence requires that accusation, formal charging, decisions about evidence, and imposition of penalties should be clearly separated. This has not happened in the case of Ward Churchill. The CU administration, usually in the person of Provost Philip DiStefano, has functioned as Churchill’s accuser, grand jury, tribunal selector, and sentencing judge. This concatenation of roles makes it easy for political motivations to penetrate the process of adjudication. While a charade of academic due process has been maintained, the treatment of Ward Churchill strongly resembles a political lynching. The plagiarism charges against Professor Churchill are superannuated, unproven, substantively inconsequential, and either wrongheaded or misdirected. His reputation as a scholar has suffered egregiously and unjustifiably as a consequence.

Due to my own involvement in his defense, I have talked to many people about the Ward Churchill affair. Most of these interactions have been disheartening to say the least. Among other things, I have received a considerable number of hate letters and e-mails characterized mainly by inarticulate rage and vulgarity. More discouraging, however, is the response of many purported liberals who claim to support academic freedom and who know something about the history of McCarthyism. Usually these individuals are completely unfamiliar with Churchill’s work and misunderstand the “little Eichmanns” phrase that is reiterated ad nauseam in the media. Knowing that a panel of reputable academics has found him guilty of plagiarism, all concern for academic freedom vanishes and my liberal interlocutors often express contempt for Churchill and support draconian penalties. They fear that the reputation of liberalism might suffer from support of a proven plagiarizer. They recoil from thinking that a panel of reputable academics could be swayed by private animosity or the prevailing political climate. Only with the greatest reluctance do these purported liberals consider contrary arguments or evidence. During these interactions I become painfully aware of how profoundly both Professor Churchill and freedom of critical thought have been wounded by this politically inspired inquisition. A just monetary compensation for Ward Churchill would be very expensive indeed. The damage to freedom of thought may be irreparable in the near future.

in june, professor norman finkelstein was denied tenure by depaul university thanks to a concerted effort by alan dershowitz. today, the university of colorado fired tenured professor ward churchill thanks to an effort by the horowitz-ACTA crowd.

i remember long ago reading an essay by stephen king in which he instructed his readers how to act when they've heard of a case of censorship: to immediately get the censored material and read it. censorship usually targets interesting and relevant ideas. finkelstein and churchill have not been censored, but they have been punished for their political views by a system that is supposed to reward intellectual accomplishment and protect the academy from political intimidation. for the enemies of critical thought, actual censorship is not a viable short-term goal, so they are instead making inroads into a more manageable goal: distorting academic debate by intimidating faculty who are independent-minded and critical in tone.

in the case of finkelstein and churchill, i happen to have read extensively of both of their works, and i recommend them without reservation. they are two of the sharpest analytical minds that i've ever read, and they both write clearly and engagingly on important topics. it is partly for these reasons that they are being targeted by the enemies of intellect. for these reasons i suggest that the appropriate response to this particular attack on critical thinking is to read these authors.

neither decision was plausible on its merits. in finkelstein's case, there was no pretense of applying the universal standards for tenure - quality of teaching and research. he was denied tenure for his "tone". if this seems like a subjective non-standard, that's because it is. he was denied tenure because conservatives don't like what he writes, and because twice he's made the conservative intellectual establishment look very, very foolish. first as a graduate student, by exposing joan peters' anti-palestinian propaganda tome "from time immemorial" as a fraud; then by demonstrating the extraordinary stupidity and absence of merit in alan dershowitz's anti-palestinian book "the case for israel".

in churchill's case, there was a pretense of applying a reasonable standard - he was accused of research misconduct. but the pretense is transparent. the president of the university who recommended his termination is a right-wing ideologue who belongs to ACTA, a highly ideological group, founded by lynne cheney and joe lieberman, dedicated to opposing critical thinking in the academy about history and politics. when it became public knowledge a few years ago that churchill had written a highly inflammatory essay about 9-11, the university president promised to subject churchill's writings to an extraordinary level of scrutiny, and convened a committee that did so. in a report that is itself subject to complaints of misconduct (but has not been investigated), the committee concluded that churchill had plagiarized and falsified information relating to native american history, though not in any scholarly writing. the faculty panel charged with making a recommendation recommended against dismissing prof. churchill. as prof. gary leupp has suggested, if "boards of regents in this country were to investigate and punish the falsification of Native American history by scholars, or if society in general were to investigate such falsification in the media, popular culture and political discourse, we’d all be in for a very time-consuming process resulting in a whole lot of people out of jobs." the president, however, overruled the faculty's recommendation and recommended dismissal to the university's board of regents, which rubber-stamped his recommendation 8-1, with no public debate.

these attacks on the academy can't be seen separately from the ascendancy of fascism generally, including the bush administration's war on civil liberties, the erosion of institutions and laws intended to protect us from centralized power, and the increasing concentration of wealth and centralization of power, in this country and worldwide. follow my recommendation, do yourself and the world a favor, and read finkelstein and churchill.

7/23/07

i’ve been emphasizing, including in this blog, that exceptives can only be licensed by universals. that’s what i believed until less than an hour ago. i now think that exceptives are licensed by members of a semantic class that corresponds to roberto zamparelli’s strong determiners (see his 1995 rochester dissertation). interestingly, membership in this class, as zamparelli pointed out, has a syntactic correlate, since strong determiners appear to occur in a DP shell that encompasses the phrase projected by the other class of determiners, predicative determiners. this is evidenced in the general possibility of cooccurrence of strong and predicative determiners, with the strong determiner always linearly preceding the predicative one in english. membership in the class seems to correspond to the acceptability of phrases like the following, with “Det” standing in for the determiner:

some of these, of course, are not a single determiner but a combination of a determiner and another determiner (five), superlative adjective (tallest, arguably most/least), or uniquely identifying adjective (only). also possible are combinations of three elements when the third is a cardinal, like the tallest three or the only five.

here are some predicative determiners:

somea/anfivemanyfew

notice how they fare with respect to licensing exceptives.

every/each president was protestant, except kennedyall the presidents were protestant, except kennedyno president was protestant, except kennedythe forty-three presidents so far have been protestant, except kennedythe first three/last three presidents were protestant, except kennedythe only four presidents to have presided over the vietnam war were protestant, except kennedythe tallest presidents have been protestant, except kennedy.most of the high schoolers helped out, except the tenth gradersmy five rabbits are herbivorous, except fluffy.i don’t eat any vegetables except kale (negative polarity any)i would eat any vegetable except kale (free choice any)

the predicative determiners fare considerably worse.

*some presidents are protestant, except kennedy*a president is protestant, except kennedy*five presidents have been protestant, except kennedy*many presidents have been protestant, except kennedy*few presidents have been protestant, except kennedy

(i’m fudging a bit here; few and maybe many seem to fall in the same category as most:few of the high schoolers helped out, except the tenth gradersmany of the high schoolers helped out, except the tenth graders)

what about the “Det friend that i have” construction? here are the strong determiners

every friend that i have is a menschall the friends that i have are mensches?each friend that i have is a menschno friend that i have is a menschthe five friends that i have are menschesthe first three/the last friends that i’ve had were menschesthe only friend that i have is a menschthe tallest friend that i have is a menschmost friends that i have are mensches*my five friends that i have are mensches?don’t insult any friend that i have (negative polarity any)any friend that i have is a mensch (free choice any)

a couple are somewhat odd, and “my five” is ungrammatical, presumably for the independent reason that “my N “ doesn’t combine well with restrictive relatives. as a whole, the class of strong determiners does well in this construction.

predicative determiners do less well:

*some friends that i have are mensches*a friend that i have is a mensch*five friends that i have are mensches*many friends that i have are mensches?few friends that i have are mensches

7/21/07

some of you who know me know that one of my charming quirks is that i don't believe in empirical induction. i don't mean in hume's sense - it's not just that i don't think induction leads to weaker inferences than deduction. my skepticism is this: i don't believe that induction exists as an independent mode of reasoning. i believe that there is nothing gained by adding induction to our reasoning toolbox, because anything that it does is already covered by abduction. since there are things covered by abduction that are not covered by induction, it is induction that is redundant.

my initial formulation of induction is as follows:

for every individual P and attribute X, frequent observation that an instance of P has attribute X, with no observation that P lacks attribute X, licenses the inference that every P has attribute X.

i don't think much of the critique is contingent on this particular formulation; i welcome feedback on it.

i can think of four arguments against induction, but i don't have good names for them at the present. i'm aware from personal experience and from reading feyerabend that good marketing is essential to philosophical and scientific progress, so i will start trying to think up some good names - maybe get burson-marsteller to do some pro bono work on my behalf. in the meantime, here are the names of the arguments.

1. the raven paradox argument2. the argument from the structure of logic3. the unvarying datum argument4. the clash with theory argument

in this post i'll give very quick summaries. i'll plan to elaborate in the future.

1. the raven paradox argument

take the following proposition:

(p) every raven is black

(p) is logically equivalent to (p')

(p') every non-black thing is not a raven

if induction is valid, then observing many black ravens lets us infer (p) (and (p')). so far, so good. but observing many non-black non-ravens also lets us infer (p) (and (p')), and this goes against our understanding of what good evidence is. right now i can see an orange curtain, a greyish ceiling fan and white walls. they are not good evidence that all ravens are black, but induction suggests that they are.

this argument, due to hempel, has generated a number of solutions intended to rescue induction. i don't think they're very good, and i hope to address them in the future. i believe my approach - to dump induction in the harbor - makes more sense.

2. the argument from the structure of logic

logic is about drawing conclusions from premises using formal rules. the rules are rigid, while the premises and conclusions vary. i suggest that this restricts the modes of reasoning to two: given premises, reasoning to conclusions - this is deduction; and given conclusions, hypothesizing premises - this is abduction. there is no room for other modes of reasoning like induction. it is possible, of course, that induction is a submode of abduction; but if induction is to not be redundant, then the burden is on its advocates to show that it has interesting properties that set it apart from ordinary abduction.

3. the unvarying datum argument

suppose P has two subtypes: P' and P''. and suppose we observe, frequently and unvaryingly, that instances of P' have attribute X. does this license an inference that all P have attribute X? by induction, it does. and then it follows that all instances P'', about which we've observed nothing, have attribute X. this is preposterous.

the same situation arises with respect to a P with no subtypes, but which could in principle be observed under different conditions but is observed in only one kind of condition. suppose that in all the observations, P has attribute X. induction would lead us to believe that every P has attribute X, without accounting for the possibility that it is an artifact of the conditions of observation.

4. the clash with theory argument

induction allows us to infer that the sun will rise tomorrow. suppose we have a very good theory of the cosmos which predicts with certainty that before tomorrow, the earth will stop rotating, or else that the sun will explode. it is rational to believe the theory rather than our past experience. but induction allows us to infer that the sun will rise tomorrow. so induction licenses an irrational inference.

feedback welcome.

EDIT: how could i forget the grue argument of nelson goodman?

5. the grue argument

define the attribute grue as follows.

for some time t and all P, P is grue iff it is green if observed before t and blue if not observed before t.

if some P has been observed before t, then induction allows us to infer with equal probability at t that P is green and that P is grue. this means that it predicts with equal force that P will appear green and that P will appear blue next time it is observed.

7/17/07

earlier i raised the following challenge to the generalization that only universals admit of exceptions:

most of the students helped out, except the tenth graders

the challenge is that exceptive phrases are pretty well established as applying to universals, and most is not a universal.

i suggested a solution: that there should be understood a presupposed partition on the set of students, based on grade. so that the sentence can be restated as follows:

given a partition of the students into equivalence classes based on grades, every equivalence class except the one consisting of the tenth graders is such that most of its members helped out.

this solves the problem of the universal by introducing one, albeit an invisible one, to license the exceptive. it also gets the truth conditions of the sentence right. but it is a challenging approach, because in the absence of independent justification for an invisible presupposed partition and universal quantifier, it is a rather ad hoc solution. in this post i try to support the analysis by bringing one source of independent evidence for an invisible universal, from negative polarity item licensing.

i noted in my previous post that most differs from other quantifiers, such as some.

*some of the students helped out, except the tenth graders

recently i remembered the fact, discussed in the literature on polarity items*, that some and most have different properties as far as licensing any. most licenses it sort of, while some doesn't.

most (of the) people with any self-respect abhor imperialism*some (of the) people with any self-respect abhor imperialism

i'm generally a believer in semantic and pragmatic licensing of polarity items (as opposed to, say, syntactic licensing), though not a firm believer. i don't see pragmatics as being a licenser in this case, so let's assume it's semantics. usually, negative polarity items (which we'll assume any is here. why? cause fuck free choice any, that's why) are assumed to be licensed in downward-entailing contexts. the first argument of most is not generally seen as a downward-entailing context, because of facts like the following.

most high school students are evil-/->most tenth-graders are evil

but what if these sentences were interpreted as i've suggested, as universal statements ranging over equivalence classes of a presupposed partition? and what if the set expressed in the consequent was one of the equivalence classes presupposed in the antecedent? in that case, there would be an entailment.

given a partition of the set of high schoolers by grade, for every equivalence class E, for most x, x a high school student in E, x is evil.

-->

given a partition of the set of high schoolers by grade, for every equivalence class E, for most x, x a tenth-grader in E, x is evil.

if this universal interpretation is available, it helps us solve the puzzle of why most is a sort-of licenser of any. It's because most is sort of downward-entailing in its first argument, because it is sort of a universal quantifier.

now, the same would be true of some. If it was susceptible to a universal interpretation, it would be as downward-entailing as most is in the example just given. We would then expect it to license both an exceptive and any in its first argument. but it does neither, which we can attribute to its inability to accommodate to a universal interpretation.

the larger mystery, of why most can do what other quantifiers can't, still exists. but at least we've suggested a connection between two properties: licensing of any and support for exceptives.

this approach is surely wrong. and you know what? that doesn't bother me, because i don't have to publish in linguistics anymore.

-=-=-=-=-=-=-=-=--=-* i would guess this is in myriam uribe-echebarria's dissertation, for instance.